Remarks on the \(L^ 2\)-cohomology of singular algebraic surfaces (Q1825921)
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scientific article; zbMATH DE number 4122118
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remarks on the \(L^ 2\)-cohomology of singular algebraic surfaces |
scientific article; zbMATH DE number 4122118 |
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Remarks on the \(L^ 2\)-cohomology of singular algebraic surfaces (English)
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1989
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Let X be a normal algebraic surface with singular set S and \({\mathcal X}=X- S\). Then a theorem due to Hsiang-Pati shows that the \(L^ 2\)-cohomology \(H^ i_{(2)}({\mathcal X})\) is naturally isomorphic to the dual of the middle intersection homology \(IH^ m_ i(X)\). The author examines this result in detail and fills a gap.
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Fubini-Study metric
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normal algebraic surface
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\(L^ 2\)-cohomology
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intersection homology
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